13y^2+21y=-5y^2+22

Solution for 13y^2+21y=-5y^2+22 equation:

13y^2+21y=-5y^2+22

We move all terms to the left:

13y^2+21y-(-5y^2+22)=0

We get rid of parentheses

13y^2+5y^2+21y-22=0

We add all the numbers together, and all the variables

18y^2+21y-22=0

a = 18; b = 21; c = -22;
Δ = b2-4ac
Δ = 212-4·18·(-22)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-45}{2*18}=\frac{-66}{36}
=-1+5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+45}{2*18}=\frac{24}{36}
=2/3
$